Support NoteClass

Remodel application to support the scientific pitch notation for notes. Instead
of supporting simply "C", support "C4". This change created cascading
changes. After refactoring for around an hour, I restored the app to a working
state. The current state is not desirable, but it compiles. More changes on the
way.

1 files changed, 132 insertions, 77 deletions

diff --git a/website/sandbox/chord-drill-sergeant/src/Theory.elm b/website/sandbox/chord-drill-sergeant/src/Theory.elm
index 4a275fa79e1f..9e84aeac4c4e 100644
--- a/website/sandbox/chord-drill-sergeant/src/Theory.elm
+++ b/website/sandbox/chord-drill-sergeant/src/Theory.elm
@@ -1,6 +1,7 @@
 module Theory exposing (..)
 
 import List.Extra
+import Misc
 
 {-| Notes are the individuals sounds that we use to create music. Think: "do re
 mi fa so la ti do".
@@ -13,18 +14,29 @@ Note: There are "notes" like A, B, D-flat, and then there are notes like "middle
 C", also denoted in scientific pitch notation as C4. I'm unsure of what to call
 each of these, and my application does not model scientific pitch notation yet,
 so these non-scientific pitch denote values are "notes" for now. -}
-type Note = C
-          | C_sharp
-          | D
-          | D_sharp
-          | E
-          | F
-          | F_sharp
-          | G
-          | G_sharp
-          | A
-          | A_sharp
-          | B
+type Note = C1 | C_sharp1 | D1 | D_sharp1 | E1 | F1 | F_sharp1 | G1 | G_sharp1 | A1 | A_sharp1 | B1
+          | C2 | C_sharp2 | D2 | D_sharp2 | E2 | F2 | F_sharp2 | G2 | G_sharp2 | A2 | A_sharp2 | B2
+          | C3 | C_sharp3 | D3 | D_sharp3 | E3 | F3 | F_sharp3 | G3 | G_sharp3 | A3 | A_sharp3 | B3
+          | C4 | C_sharp4 | D4 | D_sharp4 | E4 | F4 | F_sharp4 | G4 | G_sharp4 | A4 | A_sharp4 | B4
+          | C5 | C_sharp5 | D5 | D_sharp5 | E5 | F5 | F_sharp5 | G5 | G_sharp5 | A5 | A_sharp5 | B5
+          | C6 | C_sharp6 | D6 | D_sharp6 | E6 | F6 | F_sharp6 | G6 | G_sharp6 | A6 | A_sharp6 | B6
+          | C7 | C_sharp7 | D7 | D_sharp7 | E7 | F7 | F_sharp7 | G7 | G_sharp7 | A7 | A_sharp7 | B7
+          | C8
+
+{-| I alluded to this concept in the Note type's documentation. These are the
+letters of notes. For instance C2, C3, C4 are all instances of C. -}
+type NoteClass = C
+               | C_sharp
+               | D
+               | D_sharp
+               | E
+               | F
+               | F_sharp
+               | G
+               | G_sharp
+               | A
+               | A_sharp
+               | B
 
 {-| Encode whether you are traversing "up" or "down" intervals -}
 type StepDirection = Up | Down
@@ -67,7 +79,7 @@ type ChordPosition = First
 {-| Songs are written in one or more keys, which define the notes and therefore
 chords that harmonize with one another. -}
 type alias Key =
-  { note : Note
+  { noteClass : NoteClass
   , mode : Mode
   }
 
@@ -80,48 +92,35 @@ type Mode = BluesMode
           | MajorMode
           | MinorMode
 
+{-| Returns the Note in the cental octave of the piano for a given
+NoteClass. For example, C4 -- or "middle C" -- for C. -}
+noteInCentralOctave : NoteClass -> Note
+noteInCentralOctave noteClass =
+    case noteClass of
+        C       -> C4
+        C_sharp -> C_sharp4
+        D       -> D4
+        D_sharp -> D_sharp4
+        E       -> E4
+        F       -> F4
+        F_sharp -> F_sharp4
+        G       -> G4
+        G_sharp -> G_sharp4
+        A       -> A4
+        A_sharp -> A_sharp4
+        B       -> B4
+
 {-| Return the note that is one half step away from `note` in the direction,
 `dir`.
+In the case of stepping up or down from the end of the piano, this returns a
+Maybe.
 -}
-halfStep : StepDirection -> Note -> Note
+halfStep : StepDirection -> Note -> Maybe Note
 halfStep dir note =
-  case (dir, note) of
-    -- C
-    (Up, C) -> C_sharp
-    (Down, C) -> B
-    -- C#
-    (Up, C_sharp) -> D
-    (Down, C_sharp) -> C
-    -- D
-    (Up, D) -> D_sharp
-    (Down, D) -> C_sharp
-    -- D_sharp
-    (Up, D_sharp) -> E
-    (Down, D_sharp) -> D
-    -- E
-    (Up, E) -> F
-    (Down, E) -> D_sharp
-    -- F
-    (Up, F) -> F_sharp
-    (Down, F) -> E
-    -- F#
-    (Up, F_sharp) -> G
-    (Down, F_sharp) -> F
-    -- G
-    (Up, G) -> G_sharp
-    (Down, G) -> F_sharp
-    -- G#
-    (Up, G_sharp) -> A
-    (Down, G_sharp) -> A
-    -- A
-    (Up, A) -> A_sharp
-    (Down, A) -> G_sharp
-    -- A#
-    (Up, A_sharp) -> B
-    (Down, A_sharp) -> A
-    -- B
-    (Up, B) -> C
-    (Down, B) -> A_sharp
+  case dir of
+    Up   -> Misc.comesAfter note allNotes
+    Down -> Misc.comesBefore note allNotes
+
 {-| Return a list of steps to take away from the root note to return back to the
 root note for a given mode.
 -}
@@ -148,49 +147,105 @@ intervalsForChordType chordType =
     Diminished7    -> [MinorThird, MinorThird, MinorThird]
 
 {-| Return the note in the direction, `dir`, away from `note` `s` intervals -}
-step : StepDirection -> Interval -> Note -> Note
+step : StepDirection -> Interval -> Note -> Maybe Note
 step dir s note =
   let
     doHalfStep = halfStep dir
   in
     case s of
-      Half       -> doHalfStep note
-      Whole      -> doHalfStep note |> doHalfStep
-      MinorThird -> doHalfStep note |> doHalfStep |> doHalfStep
-      MajorThird -> doHalfStep note |> doHalfStep |> doHalfStep |> doHalfStep
+      Half ->
+          doHalfStep note
+      Whole ->
+          doHalfStep note
+              |> Maybe.andThen doHalfStep
+      MinorThird ->
+          doHalfStep note
+              |> Maybe.andThen doHalfStep
+              |> Maybe.andThen doHalfStep
+      MajorThird ->
+          doHalfStep note
+              |> Maybe.andThen doHalfStep
+              |> Maybe.andThen doHalfStep
+              |> Maybe.andThen doHalfStep
 
-{-| Returns a list of all of the notes up from a give `note` -}
-applySteps : List Interval -> Note -> List Note
+{-| Returns a list of all of the notes up from a give `note`.
+
+In the case where applying all of the steps would result in running off of the
+edge of the piano, this function returns a Maybe. -}
+applySteps : List Interval -> Note -> Maybe (List Note)
 applySteps steps note =
-  case List.foldl (\s (prev, result) -> ((step Up s prev), (step Up s prev :: result))) (note, []) steps of
-    (_, result) -> List.reverse result
+    doApplySteps steps note [] |> Maybe.map List.reverse
+
+doApplySteps : List Interval -> Note -> List Note -> Maybe (List Note)
+doApplySteps steps note result =
+    case steps of
+        [] -> Just (note::result)
+        s::rest ->
+            case step Up s note of
+                Just x -> doApplySteps rest x (note::result)
+                Nothing -> Nothing
+
+{-| Return the NoteClass for a given note. -}
+classifyNote : Note -> NoteClass
+classifyNote note =
+    if List.member note [C1, C2, C3, C4, C5, C6, C7, C8] then
+        C
+    else if List.member note [C_sharp1, C_sharp2, C_sharp3, C_sharp4, C_sharp5, C_sharp6, C_sharp7] then
+        C_sharp
+    else if List.member note [D1, D2, D3, D4, D5, D6, D7] then
+        D
+    else if List.member note [D_sharp1, D_sharp2, D_sharp3, D_sharp4, D_sharp5, D_sharp6, D_sharp7] then
+        D_sharp
+    else if List.member note [E1, E2, E3, E4, E5, E6, E7] then
+        E
+    else if List.member note [F1, F2, F3, F4, F5, F6, F7] then
+        F
+    else if List.member note [F_sharp1, F_sharp2, F_sharp3, F_sharp4, F_sharp5, F_sharp6, F_sharp7] then
+        F_sharp
+    else if List.member note [G1, G2, G3, G4, G5, G6, G7] then
+        G
+    else if List.member note [G_sharp1, G_sharp2, G_sharp3, G_sharp4, G_sharp5, G_sharp6, G_sharp7] then
+        G_sharp
+    else if List.member note [A1, A2, A3, A4, A5, A6, A7] then
+        A
+    else if List.member note [A_sharp1, A_sharp2, A_sharp3, A_sharp4, A_sharp5, A_sharp6, A_sharp7] then
+        A_sharp
+    else
+        B
 
 {-| Return a list of the notes that comprise a `chord` -}
-notesForChord : Chord -> List Note
+notesForChord : Chord -> Maybe (List Note)
 notesForChord {note, chordType} =
-  note :: applySteps (intervalsForChordType chordType) note
+    case applySteps (intervalsForChordType chordType) note of
+        Nothing -> Nothing
+        Just notes -> Just <| note::notes
 
 {-| Return the scale for a given `key` -}
 notesForKey : Key -> List Note
-notesForKey {note, mode} =
-  applySteps (intervalsForMode mode) note
+notesForKey {noteClass, mode} =
+    let origin = noteInCentralOctave noteClass
+    in case applySteps (intervalsForMode mode) origin of
+           -- We should never hit the Nothing case here.
+           Nothing -> []
+           Just scale -> scale
+
+{-| Return a list of all of the notes that we know about. -}
+allNotes : List Note
+allNotes =
+  [ C1 , C_sharp1 , D1 , D_sharp1 , E1 , F1 , F_sharp1 , G1 , G_sharp1 , A1 , A_sharp1 , B1
+  , C2 , C_sharp2 , D2 , D_sharp2 , E2 , F2 , F_sharp2 , G2 , G_sharp2 , A2 , A_sharp2 , B2
+  , C3 , C_sharp3 , D3 , D_sharp3 , E3 , F3 , F_sharp3 , G3 , G_sharp3 , A3 , A_sharp3 , B3
+  , C4 , C_sharp4 , D4 , D_sharp4 , E4 , F4 , F_sharp4 , G4 , G_sharp4 , A4 , A_sharp4 , B4
+  , C5 , C_sharp5 , D5 , D_sharp5 , E5 , F5 , F_sharp5 , G5 , G_sharp5 , A5 , A_sharp5 , B5
+  , C6 , C_sharp6 , D6 , D_sharp6 , E6 , F6 , F_sharp6 , G6 , G_sharp6 , A6 , A_sharp6 , B6
+  , C7 , C_sharp7 , D7 , D_sharp7 , E7 , F7 , F_sharp7 , G7 , G_sharp7 , A7 , A_sharp7 , B7
+  , C8
+  ]
 
 {-| Return a list of all of the chords that we know about. -}
 allChords : List Chord
 allChords =
-  let notes = [ C
-              , C_sharp
-              , D
-              , D_sharp
-              , E
-              , F
-              , F_sharp
-              , G
-              , G_sharp
-              , A
-              , A_sharp
-              , B
-              ]
+  let notes = allNotes
       chordTypes = [ Major
                    , Major7
                    , MajorDominant7